A cable hanging vertically under gravity must support its weight, w = mg, where m is the mass of the cable and g = 9.8 m/s2 is the acceleration due to gravity. If the cable has a cross sectional area A, length ℓ, and density ?, then the weight of the cable is w = ?Aℓg. The force per unit area at the top of the cable is then T = ?ℓg. Steel has a tensile strength 2 GPa and a density 7.8 x 103 kg/m. If the force per unit area at the top of a hanging cable exceeds the tensile strength, it will snap. Given this, estimate the maximum length of a hanging steel cable.

Q: A solid copper cube has an edge length of 89.6 cm. How much stress must be applied to the cube to…

A: Write the given values with the suitable variables. Li=89.6 cmLf=89 cmk=1.4×1011 N/m2 Here, Li, Lf,…

Q: A 2.5 meter metal column has a 4500kg load placed on it and it compresses 0.0016 meters.  If the…

A: The Young's modulus is given by, Y=stressstrain The stress is given by, stress=FA Here, F is the…

Q: Steel beams are used for load bearing supports in a building. Each beam is 4.0 m long with a…

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Q: A metal rod is 4.00m long and has a cross-sectional area of 0.50cm^2. It stretches 0.20cm under a…

A: Given data:  Original Length (L) = 4.00 m Cross section area (A) = 0.50 cm2 = 0.50×10-4 m2 Stretch…

Q: A cylindrical specimen of some metal alloy of 8.5 mm in diameter is stressed elastically in tension.…

A: Given  T = 15700 N. D = 8.5 mm = 0.0085 m ∆D = 5.3*10-3mm

Q: By applying 2.00 x 106 N/m2 shear stress to a steel bar 2 m in length, calculated the shear bending…

A: Shear Bending Stress(S) for steel is given as,    S=(8.3×108 N/m2)=Shear StressShear strain

Q: A circular rod of cross-sectional area 2 x 10m² has a tensile force of 80 kN applied to it. The…

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Q: 29. A steel wire of length 2.0 m and diameter 1.01 mm is fixed at its upper end and its lower end…

A: The given data are: L=2 md=1.01 mm=1.01×10-3 mm=400 g=0.4 kgE=2×1011 Pa Here, L denotes the length,…

Q: An object with a mass equal to 300 kg is hung on a wire of length 5.00 m and cross-sectional area of…

A: Write the given values with suitable variables. m=300 kgL=5 mA=0.25×10-4 m2E=8×1010 N Here, m is the…

Q: A 2 m long steel rod has a cross-sectional area of 0.3 cm?. The rod is a part of a vertical support…

A: The stress of the rod is given by F/A Strain is given by dL/L                    where F= Force…

Q: The following figures show a steel bars of thickness h = 5 mm. the bars are subjected to a force P.…

A: Given: Figures with thickness, h = 5 mm Shear stress, t = 140MPa

Q: A solid copper cube has an edge length of 89.6 cm. How much stress must be applied to the cube to…

A:

Q: A solid copper cube has an edge length of 89.3 cm. How much stress must be applied to the cube to…

A:

Q: The modulus of elasticity of a certain steel material is 200 GPa (Giga Pascal). What is the strain…

A: Modulus of elasticity for a material is defined as the ratio of stress to strain in a body. In this…

Q: Human bones have a Young's modulus of 1.5 x 1010 Pa. The bone breaks if stress exceeds 1.5 x 10° Pa.…

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Q: A nylon string on a tennis racket is under a tension of 275 N. If the string's radius is 5.00 x 10-4…

A: The equation for the change in length can be obtained from equation for the Young’s Modulus as

Q: A 50-N force is applied to a metal rod with a length of 10 m and a cross- sectional area of 1.0 x…

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Q: A copper wire of length 5.9 m , cross sectional area 2.6 x 10-6m2and Young’s modulus 11 x 1010 N/m2…

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Q: A cable is 10.0 m long and has a diameter of 2.00 mm. A force of 45.0 N is applied to the end of the…

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Q: 20. A 20-m long steel wire (cross-section 1.0 cm2, Young's modulus 2.0 x 10I N/m²), is subjected to…

A: Given that Original length of wire L = 20 m Cross section area A = 1 cm2 = 1 X 10-4 m2 Young's…

Q: A solid copper cube has an edge length of 89.9 cm. How much stress must be applied to the cube to…

A: The ratio of volumetric stress with volumetric strain is defined as the bulk modulus. To solve the…

Q: A violin string has a radius of 4.1 x 104m. During tuning, 32.5 cm of the string is placed under a…

A: Given Initial lenth of string is 32.5 cm Elongation of lenth is 0.93 cm Assume elongation in elastic…

Q: 1. Rank the following materials based on its rigidity, where 1 is the most rigid and 3 is the least…

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Q: A copper wire of length 7.9 m , cross sectional area 2 x 10-m²and Young's modulus 11 x 1010 N/m² has…

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Q: The upper surface of a cube of gelatin, 5.0 cm on a side, is displaced by 0.64 cm by a tangential…

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Q: 2. A 4.0 m long copper wire of cross-sectional area 2 2 cm is stretched by a force of 4.8 x 10° N.…

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Q: A steel WIre of diameter I mm can support a tension of0.2 kN. À cable to support a tension of 20 kN…

A: Given : Diameter of first steel wire, d1 = 1 mm Tension the first wire can support, T1 = 0.2kN…

Q: The pressure increases by 1.0 x 104 N/m2 for every meter of depth beneath the surface of the ocean.…

A: Given: The increase in pressure is 1.0×104 N/m2 per meter. The bulk modulus of Pyrex is 2.6×1010…

Q: 1 m wire has a cross sectional area 10-4 m2. The wire is stretched by a load of 50 kg causing it to…

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Q: The bulk modulus of a material is 5.62 × 1011 N/m2. What fractional change in volume does a piece of…

A: bulk modulus of a material is 5.62 × 1011 N/m2. What fractional change in volume does a piece of…

Q: Find the density of seawater at a depth where the pressure is 460 atm if the density at the surface…

A: Pressure , P = 460 atm  Density , ρ= 1100 kg/m3  Bulk modulus , B = 2.3 x 109  To find =density at…

Q: A steel cable 3.00 cm2 in cross-sectional area has a mass of 2.40 kg per meter of length. If 500 m…

A: The expression for the ratio of the change in length to that of the original,

Q: A shear force of 2300 N is applied on a cube of side length 0.50 m, causing it to deform through an…

A:

Q: A 0.50 m long guitar string, of cross- sectional area 1.0 x10-6 m2, has a Young’s modulus of 2.0x…

A: Given : L = 0.50 m A = 1 × 10-6 m2 Y = 2 × 109 Pa F = 20.0 N

Q: What force is required to stretch a steel wire 1 cm² in cross section to double its length, if…

A: When a force is applied at the end of the material gets deformed and the molecules of the material…

Q: Find the minimum diameter of a nylon wire 50 m long that will stretch no more than 25 cm when a load…

A: Given that, length of the nylon, L =50 m stretch length , l =25 cm =0.25 m mass, m =90 kg Y nylon…

Q: A 469 kg load is hung on a wire of length 6 m, cross- sectional area 0.200 x 10¬ 4 m², and Young's…

A: Given : m = 469 kg L = 6 m A = 0.200 × 10-4 m2 Y = 8 × 1010 N/m2

Q: A steel rod 55 cm long has a diameter of 30.0 cm.  The compressive strength (the maximum stress it…

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Q: A 439 kg load is hung on a wire of length 9 m, cross-sectional area 0.200 x 10–4 m2, and Young's…

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Q: 7. The ultimate strength in compression of an object is 3.0 x 10^7 Pa. Find the maximum mass that…

A: Given  Ultimate strength σ=3×107 Pa Area A=0.125 cm2

Q: A piece of steel has a height of ten meters and a unit cross-sectional area of 5.0 m³. It supports a…

A: Given: The length of the steel is L=10 m. The cross-sectional area is A=5 m3. The mass is m=30,000…

Q: A man with a mass of 71.6 kg stands on one foot. His femur has a cross-sectional area of 8.00 cm2…

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Mechanical Properties of Solids

There are three types of matter- solid, liquid and gas. Out of them, solids have a rigid shaped and size. The intermolecular forces of attractions in solids are greatest. Mechanical properties are the physical properties of a material which it shows, when it is provided with certain amount of force or load. These properties are to be kept in mind for various purposes. When a force is applied to an object, the object may or may not get deformed depending upon its elastic property. But every time the object develops a restoring force against the force applied. This is commonly known as stress. If the object changes its dimensions due to the force applied it develops strain ( which is the ratio of change in dimension to the original dimension).